The present invention relates to a Reed-Solomon code generator and, more particularly, to one which finds various applications such as to pulse code modulation (PCM) recording/playback apparatuses, on which audio video and other information signals are digitally processed, employing magnetic tapes or discs, and to other digital signal recording/playback apparatuses for checking or correcting code errors caused in the digital signals processed in the apparatuses.
The principle of Reed-Solomon code generation which prior art generators have employed will be described first.
Assume that parity words P and Q are generator for "k" externally derived data words W.sub.1 -W.sub.k, and that (k+2, k) Reed-Solomon codes are prepared with W.sub.1 -W.sub.k, P and Q. Also, assume that the parity matrix for Reed-Solomon codes is ##EQU1## where .alpha. is the primitive root of a predetermined polynomial, and [S.sub.0, S.sub.1 ].sup.T is the syndrome (T indicates displacement of matrix). Therefore, when k=14 for example, and if all the external data words and parity words W.sub.1, W.sub.2, . . . , W.sub.14, P and Q are correct, the Reed-Solomon code parity matrix ##EQU2## is expressed as EQU S.sub.0 =W.sub.1 +W.sub.2 +. . . +W.sub.14 P+Q=0 EQU S.sub.1 =.alpha..sup.15 .multidot.W.sub.1 +.alpha..sup.14 .multidot.W.sub.2. . . .alpha..multidot.P+Q=0
Even when the check matrix is modified (multiplying one row by a constant and adding the product to another row), the resulting matrix ##EQU3## is still a parity matrix. Therefore, EQU .alpha..sup.X.sbsp.1 .multidot.W.sub.1 +.alpha..sup.x.sbsp.2 .multidot.W.sub.2. . . .alpha..sup.X.sbsp.14 .multidot.W.sub.14 +1.multidot.P+0=0 EQU .alpha..sup.Y.sbsp.1 .multidot.W.sub.1 +.alpha..sup.Y.sbsp.2 .multidot.W.sub.2. . . .alpha..sup.Y.sbsp.14 .multidot.W.sub.14 +0+1.multidot.Q=0
Hence, the parity words P and Q can be calculated as EQU P=.alpha..sup.X.sbsp.1 .multidot.W.sub.1 +.alpha..sup.X.sbsp.2 .multidot.W.sub.2 +. . . +.alpha..sup.X.sbsp.14 .multidot.W.sub.14 EQU Q=.alpha..sup.Y.sbsp.1 .multidot.W.sub.1 +.alpha..sup.Y.sbsp.2 .multidot.W.sub.2 +. . . +.alpha..sup.Y.sbsp.14 .multidot.W.sub.14
However, devices heretofore proposed for accomplishing the above-described principle of Reed-Solomon code generation require a costly ROM network and is disproportionately intricate in construction.